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A general model linking environmental fluctuations and species richness is proposed. This model includes two important biological mechanisms. A first term describes the global negative effect of fluctuations on richness via stress and density-independent mortality; a second term represents the positive effect of perturbations on richness by competitive relaxation. Both effects are modeled as exponential functions. The model can be made richness-dependent putting the average competition coefficients as a function of the actual diversity. The system shows a non-trivial behavior since it has local maxima or minima in the richness function at intermediate values of environmental variability. The existence of these points depends on the ratio between stress sensitivity and competition coefficients. The discrete version of the model exhibits chaotic fluctuations when the initial richness is high.